The Study Of Cubic B-spline Curves About Local Shape Adjustment Problems

Spline function plays an important role in the theory and application of the function ap-proximation.We can design and build a wide variety of curves,surfaces by the spline func-tion,especially B-spline function that has simple structure,stability to calculate easily andmore widely range of application.But in practical applications,we often need to change theshape of the curve and surface to suit diferent requirements.This article will aim at theCubic uniform B-spline Curves about local shape adjustment problems to expand research.Major works are as follows:Firstly, the paper analyzes the theory and method about previous studies related Curveshape adjustment, especially the studies of B-Spline Curve shape adjustment.Secondly, the paper studies the mean which changes the spline curve shape locally bythe method of control points with adjustment parameters.Again, the paper discusses the spline curves that have adjusted local shape bring thechanges about the curve continuity and the conditions to maintain a variety of continuity.Last, the paper provides some numerical examples on the application of parametriccurves.In the study,we present and analyze the method that generates the Cubic uniformB-spline Curves by the control points with shape adjustment parameters rather than bythe basis function containing adjustment parameters.In this method,we do not need todiscuss properties due to the use of the basis function,which it is still the Cubic uniformB-spline basis,but mainly to discuss shape adjustment parameters gives an efect on thecurve deformation.Since the most notable feature of B-spline Curve is the partial adjustableproperty, Therefore,we will focus on the work that the shape parameter changes bringabout the relevant infuence to the local shape of the curve.Also,this is the way that usecontrol points with shape parameters to achieve the proposes about the Cubic uniformB-spline Curves about local shape adjustment.In addition,we can still use this method withadjustment shape parameters to construct more the curve that can change its shape and position to meet diferent needs.